Method and device for calculating zero-croccing reference sequences for signal detection of angle-modulated signals based on zero crossings of the received signal

ABSTRACT

A method for calculating zero-crossing reference sequences ({t i }) for the data detection of a sequence of zero crossings ({{circumflex over (t)} i }) of a received signal is disclosed. The data detection is determined in a receiver, wherein the received signal is based on a data symbol sequence ({d k }) angle-modulated at a transmitter and transmitted to the receiver. The zero-crossing reference sequences ({t i }) are calculated in accordance with an equation specifying an output of a finite state machine that describes, at least approximately, the signal generation in the transmitter.

FIELD OF THE INVENTION

The present invention relates to a method and to a device forcalculating zero-crossing reference sequences for the data detection ofa sequence of zero crossings, determined in a receiver, of a receivedsignal which is based on a data symbol sequence which isangled-modulated.

BACKGROUND OF THE INVENTION

In cordless digital communication systems which are based on theBluetooth, DECT, WDCT standard or a similar standard, traditional signalprocessing methods are used for demodulating the received signal and forthe signal detection at the receiver end. Receiver designs are known inwhich the intermediate-frequency signal is converted into the digitaldomain with the aid of an analog/digital converter and the signaldetection is implemented with the aid of methods of digital signalprocessing. Using such methods, a high-quality signal detection can beachieved but it is disadvantageous that an elaborate analog/digitalconverter is needed. Such a method, which is frequently used, is basedon the so-called limiter-discriminator demodulator in which, after hardlimiting of the band-pass signal which, as a rule, is complex, thereceived angle-modulated signal is demodulated, e.g. by means of ananalog coincidence demodulator.

In the printed document DE 102 14 581.4, an intermediate-frequencyreceiver is described which uses a zero-crossing detector for the signaldetection. The zero-crossing detector measures the time intervalsbetween the zero crossings of a received intermediate-frequency signaland determines the transmitted data symbols from the zero-crossinginformation. For this purpose, the sequence of zero-crossing intervalsoutput by the zero-crossing detector is stored in digital form in ashift register chain and compared with previously stored zero-crossingreference sequences in a classification unit. A city block metric isproposed for measuring the distance between the sequences measured andthe sequences stored. The previously stored zero-crossing referencesequence which has the smallest distance from the measured zero-crossingsequence is selected. The symbol corresponding to this selectedzero-crossing reference sequence (or the symbol sequence associated withthis zero-crossing reference sequence, respectively) represents thedetected symbol (the detected symbol sequence) and thus the solution ofthe detection problem.

From the points of view of expenditure and costs, using a zero-crossingdetector is a very interesting receiver concept since it enables an(expensive) analog/digital converter to be dispensed with. The problemwith this receiver concept is that the number of zero crossings in asymbol interval fluctuates in dependence on the data and otherinfluencing variables (known system parameters, unknown interferinginfluences). For this reason, it is difficult to allocate successivezero crossings of the zero-crossing sequence measured directly to theequidistant symbol intervals. The advantage of conventional digitalreceiver concepts which have a fixed, or at least known, number ofsamples per symbol interval is thus not present in the receiver conceptwith a zero-crossing detector.

Apart from the problem of allocating zero crossings measured in thereceiver to symbol intervals, a further problem is the use ofzero-crossing detectors in the determination of zero-crossing referencesequences, by means of which a symbol-interval-related comparison withthe measured sequence of zero crossings can be managed. An inexpensiveimplementation of this receiver design based on a detection of zerocrossings of the received signal or of an intermediate-frequency signalis only made possible by as efficient as possible a form of calculatingsuch zero-crossing reference sequences.

SUMMARY OF THE INVENTION

The following presents a simplified summary in order to provide a basicunderstanding of one or more aspects of the invention. This summary isnot an extensive overview of the invention, and is neither intended toidentify key or critical elements of the invention, nor to delineate thescope thereof. Rather, the primary purpose of the summary is to presentone or more concepts of the invention in a simplified form as a preludeto the more detailed description that is presented later.

The invention is directed to a method and a device for the inexpensivecalculation of zero-crossing reference sequences for a data detectionwhich is based on the evaluation of a sequence of zero crossings,determined in the receiver, of a received signal.

Accordingly, the zero-crossing reference sequences are calculated inaccordance with an equation specifying the output of a finite statemachine (FSM), the finite state machine describing at leastapproximately the signal generation in the transmitter.

According to the definition of the term by the NIST (National Instituteof Standards and Technology,http://www.nist.gov/dads/HTML/finiteStateMachine.html), a state machinewith output is a calculation model consisting of a set of states, astarting state, an input symbol alphabet, a transfer function which maps(at least) one symbol input and (at least) one current state onto a nextstate, and (at least) one output which provides output values which arecombined via an equation with state transitions and/or states of thestate machine. It is thus of significance for the invention that (1) thezero-crossing reference sequences can be described as output values ofan FSM and that (2) the equation which describes the relationshipbetween the state variables describing one state of the FSM and theoutput values of the FSM (i.e. the zero crossings) is linear. Combiningthese two measures provides for a simple calculation of thezero-crossing reference sequences which, in particular, can also beperformed efficiently in real time in the receiver.

It is pointed out that information contained in zero crossings can berepresented in various ways, e.g. as a sequence of the times of the zerocrossings or as a sequence of the time intervals between successive zerocrossings, etc. The terms zero-crossing reference sequences andsequences of zero crossings are generally meant as sequences ofcorresponding zero-crossing information, i.e. are intended to comprisethe forms of representation mentioned, and others, of informationobtained by measuring zero crossings.

If in the case of a modulation at the transmitter, a modulation memoryof length L, with L≧2, is used (this is also called a so-called partialresponse modulation method in which the spectral impulse function g(t)extends over a number of symbol intervals), the memory of the modulationis taken into consideration in linear form by the mathematical modeldefined by the FSM. The type of modulation, particularly the selectedspectral impulse function g(t) influences the linear equation whichspecifies the relationship between the state variables and the outputvalues of the FSM.

The signal, angle-modulated at the transmitter, is preferably generatedin accordance with a CPFSK (continuous phase frequency shift keying)method with continuous phase. One representative of CPFSK modulationmethods is GFSK (Gaussian frequency shift keying) which is used in,among others, Bluetooth or DECT systems. In GFSK, the relationshipbetween state variables and zero crossings is not linear so that,according to the invention, this relationship is initially linearized inorder to obtain a linear equation according to one embodiment of theinvention.

The signal angle-modulated at the transmitter can also be modulated inaccordance with a binary FSK or MSK modulation method. These twomodulation methods are also CPFSK modulation methods and thus havememory (it is known that the memory of an FSK signal is a consequence ofthe requirement for a continuous phase). However, the modulation formsof binary FSK and MSK differ from GFSK in that in these, an inherentlylinear relation exists between the state variables and the zerocrossings of the zero-crossing sequences. When the finite state machineaccording to the invention is used, no approximation error will thusoccur in this case.

The zero-crossing reference sequences calculated in the manner accordingto the invention can be used for a demodulation method for determiningthe transmitted data symbol sequence. For this purpose, thezero-crossing reference sequences calculated according to the inventionare compared with the detected sequence of zero crossings and thetransmitted data symbol sequence is determined by means of the resultsof the comparison.

A first advantageous embodiment of a demodulation method comprisescomparing a part-sequence of finite length of the detected sequence ofzero crossings with the zero-crossing reference sequences for each timeincrement. The method further comprises determining a data symboltransmitted in the time increment considered or a transmitted datasymbol sequence of predetermined length by means of the results of thecomparison. In this non-trellis-based procedure, in which detectiontakes place data symbol by data symbol independently of one another(i.e. without taking into consideration earlier data symbol decisions inthe current data symbol decision), the city block comparison metricdescribed in the document DE 101 03 479.3 or other analogous comparisonprocedure can be used.

A second advantageous embodiment of a demodulation method ischaracterized in that a determination of the transmitted symbolsequences is performed in accordance with the Viterbi algorithm byprocessing a trellis diagram which represents a state diagram of thefinite state machine, for each time increment, the transition metricvalues between a precursor state and a target state in the trellisdiagram being calculated by comparing the state-dependent zero-crossingreference sequences with the sequence of zero crossings detected for thetime increment considered. The advantage of efficiency of thisembodiment results from the progressive calculation of the path metricby adding the transition metric values newly calculated in each timeincrement to the path metrics of the preceding states in the knownperformance of the ACS (add compare select) operations of the Viterbialgorithm.

To the accomplishment of the foregoing and related ends, the inventioncomprises the features hereinafter fully described and particularlypointed out in the claims. The following description and the annexeddrawings set forth in detail certain illustrative aspects andimplementations of the invention. These are indicative, however, of buta few of the various ways in which the principles of the invention maybe employed. Other objects, advantages and novel features of theinvention will become apparent from the following detailed descriptionof the invention when considered in conjunction with the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

In the text which follows, the invention will be explained in greaterdetail with reference to an exemplary embodiment, referring to thedrawings, in which:

FIG. 1 is a block diagram illustrating a detector for zero crossings;

FIG. 2 is a block diagram illustrating a model of a transmission systemcomprising a transmitter, channel and receiver with a zero crossingreference sequence generator according to one embodiment of the presentinvention;

FIG. 3 is a block diagram illustrating a model of the signal generationof the interference-free sequence of zero crossings {t_(i)} with anassumed modulation memory length of L=2, and a representation of theinfluence of channel disturbances on this sequence of zero crossings;

FIG. 4 is a graph illustrating the spectral impulse function g(t), thephase function q(t) and its linear approximation q_(approx)(t) over timein units of the symbol intervals; and

FIG. 5 is a block diagram illustrating a demodulator circuit followingthe detector for zero crossings according to an embodiment of theinvention.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 shows a detector 1 for zero crossings that is supplied with ananalog angle-modulated signal 3, represented over time t, at an input 2.The analog angle-modulated signal 3 can be located, for example, in anintermediate-frequency range. The intermediate frequency should behigher than the symbol frequency so that a number of zero crossings ofthe intermediate frequency occur in each symbol period.

The detector 1 for zero crossings is a limiter-discriminator whichoutputs at its output 4 a two-valued signal 5, the zero crossings ofwhich indicate the times t₁, t₂, . . . , t₁₂, . . . of the analog inputsignal 3. Demodulation occurs on the basis of these zero crossing timest₁, t₂, . . . .

FIG. 2 shows a model of an angle-modulating transmission system. Thedata symbol sequence {d_(k)} to be transmitted is supplied to amodulator 6 at the transmitter. In the modulator 6, a suitablemodulation, for example CPFSK modulation, is performed. The phasefunction φ_(T)(t) provided by the modulator 6 is supplied to aradio-frequency section 7 of the transmitter. The radio-frequencysection 7 radiates a real-value radio-frequency signal x(t) via anantenna (not shown), the signal amplitude being designated by A_(T) andthe carrier frequency being designated by ω_(o) in FIG. 2.

The radio-frequency signal x(t) is transmitted via a multi-path channel8 which is assumed to be free of dispersion spectrally and temporally.In particular, it is assumed that no intersymbol interference (ISI)occurs. The transmission characteristic of the multi-path channel 8 isspecified by the impulse response h(t). In addition, additive channelnoise represented by the function n(t) is superimposed on thetransmitted radio-frequency signal.

The received signal r(t) received by a radio-frequency section 9 at thereceiver via an antenna (not shown) is obtained by a convolution of theimpulse response h(t) with the radiated signal x(t) with the addition ofthe noise contribution n(t). This signal is down converted into anintermediate-frequency signal y(t) in the radio-frequency section 9 ofthe receiver. In FIG. 2, A designates the amplitude of the intermediatefrequency signal, ω_(IF) designates the angular frequency of theintermediate-frequency signal, φ(t) designates the phase function andn_(φ)(t) designates a phase noise contribution of this signal. y(t) isthe reconstruction of the angle-modulated signal 3 for the detector 1for zero crossings at the receiving end.

The detector 1 for zero crossings is followed by a counter 10 whichevaluates the zero crossings of the limiter signal 5 and outputs asequence of zero-crossing times in the form of a sequence of counts{{circumflex over (t)}_(i)}. In the ideal case (no channel interference,no signal distortion on the received RF signal path), the receivedsequence of zero crossings {{circumflex over (t)}_(i)} would correspondto the sequence {t_(i)} to be expected, shown in FIG. 1.

The sequence of zero crossings {{circumflex over (t)}_(i)} measured issupplied to a symbol or symbol-sequence detector 11. Furthermore, a unit12 for generating zero-crossing reference sequences provides amultiplicity of zero-crossing reference sequences {t_(i)} for the symbolor symbol-sequence detector 11 which will be called demodulator in thetext which follows.

The elements t_(i) of the zero-crossing reference sequences {t_(i)}received in the interference-free case can be described as a map ofstate variables and thus as output of an FSM. If the modulation methodused has a memory of length L (i.e., apart from the current data symbol(bit) d_(k)), the last L data symbols d_(k-1), d_(k-2), . . . , d_(k-L)influence the functional variation of the modulated signal in thecurrent symbol interval [kT_(b), (k+1)T_(b)]), the zero crossings t_(i)in the interval [kT_(b), (k+1)T_(b)] can be represented as a function fof the state variables d_(k), d_(k-1), d_(k-2), . . . , d_(k-L) and of aphase φ_(k), where φ_(k) contains a description of the entire past up tothe time (k−L)T_(b) and is also a state variable. Therefore,t _(i) =f(d _(k) ,d _(k-1) , . . . ,d _(k-L),φ_(k)) where t _(i) ε[kT_(b),(k+1)T _(b)].  (1)

In FIG. 3, the FSM for the signal generation of the zero-crossingsequence {t_(i)} is shown for an assumed modulation memory length ofL=2. Z⁻¹ designates a delay by one symbol interval in the z space.

The unit 12 of FIG. 2 implements the FSM shown in FIG. 3; i.e. in theunit 12, the respective zero-crossing reference sequences {t_(i)} arecalculated for the possible states of the FSM (i.e. data symbols d_(k),d_(k-1), d_(k-2), . . . , d_(k-L) and phase φ_(k)) for the current timeincrement k.

Actually, in one embodiment, the function for calculating the outputvalues t_(i), forming the basis of the FSM, is predetermined by thesignal generation method (modulation method) used. If the function f islinear, it can be used according to the invention for calculating thezero crossings t_(i). If not, the relationship between the statevariables and the zero crossings t_(i), predetermined by the signalgeneration method, is linearized in accordance with the invention sothat an explicit and simple mapping rule f for calculating the zerocrossings t_(i) in the interval [kT_(b), (k+1)T_(b)] can be specifiedand is implemented in the unit 12.

The description of the zero-crossing sequence {t_(i)} as output of anFSM and the linearization of the relationship between the statevariables (d_(k), d_(k-1), d_(k-2), . . . , d_(k-L), φ_(k)) and the zerocrossings t_(i) allows the modeling of the dependence between t_(i) andd_(k), according to one embodiment of the invention, as shown in FIG. 3.This signal generation model can thus be used for describing thetransmission system shown in FIG. 2. The digital noise contributionn_(i) represents the disturbance of the zero-crossing times caused bythe analog noise contribution n(t).

In the text which follows, the transmission model shown in FIG. 2 isexplained in greater detail with the example of a GFSK modulation. Inthis explanation, the idealized interference-free case is used as abasis (since it is intended to calculate the zero-crossing referencesequences by means of this example).

The following applies for the interference-free intermediate-frequencysignal y(t) supplied to the limiter discriminator 1:y(t)=A cos(ω_(IF) t+φ(t)).  (2)

The phase

$\begin{matrix}{{\phi(t)} = {\int_{- \infty}^{t}{{\omega(\tau)}{\mathbb{d}\tau}}}} & (3)\end{matrix}$is obtained as integral over the instantaneous frequency

$\begin{matrix}{{\omega(t)} = {{\Delta\omega}{\sum\limits_{k = {- \infty}}^{\infty}{d_{k}{{g\left( {t - {kT}_{b}} \right)}.}}}}} & (4)\end{matrix}$

For the data symbols, d_(k)ε{−1,1} applies, T_(b) designates the bitperiod (equal to the symbol period in this case) and Δω designates thefrequency deviation. In GFSK, the impulse function g(t) is defined by

$\begin{matrix}{{g(t)} = {\frac{1}{2}\left\{ {{{erf}\left( {\alpha\frac{t}{T_{b}}} \right)} - {{erf}\left( {\alpha\frac{t - T_{b}}{T_{b}}} \right)}} \right\}}} & (5)\end{matrix}$where α=2/√{square root over (2 ln 2)}. The function erf (•) stands forthe Gaussian error function. The resultant phase is, from equation (3),

$\begin{matrix}{{\phi(t)} = {{\pi\eta}{\sum\limits_{k = {- \infty}}^{\infty}{d_{k}{q\left( {t - {kT}_{b}} \right)}}}}} & (6)\end{matrix}$with the index of modulation

$\begin{matrix}{\eta = {\frac{\Delta\;\omega\; T_{b}}{\pi}.}} & (7)\end{matrix}$

The phase function q(t) is then:

$\begin{matrix}{{q(t)} = {\frac{1}{T_{b}}{\int_{- \infty}^{t}{{g(\tau)}{{\mathbb{d}\tau}.}}}}} & (8)\end{matrix}$

The phase function q(t) can be specified in very good approximation inthe form

$\begin{matrix}{{q(t)} = \left\{ {\begin{matrix}{0,} & {t \leq 0} \\{q(t)} & {0 < t < {\left( {L + 1} \right)T_{b}}} \\{1,} & {t \geq {\left( {L + 1} \right)T_{b}}}\end{matrix},} \right.} & (9)\end{matrix}$where L is the length of the modulation memory.

FIG. 4 shows the spectral impulse function g(t) in the curve 20, and thephase function q(t) in the curve 21. It becomes clear that, with L=4,making the edge areas of the phase function q(t) constant according toequation (9) only causes a very slight approximation error.

Taking equation (9) into consideration, the phase variation in theinterval [kT_(b), (k+1)T_(b)] can be written as follows:

$\begin{matrix}{{{\phi(t)} = {{\pi\eta}{\sum\limits_{1 = {- \infty}}^{K}{d_{1}{q\left( {t - {1T_{b}}} \right)}}}}},\mspace{14mu}{{t \in \left\lbrack {{kT}_{b},{\left( {k + 1} \right)T_{b}}} \right\rbrack}\mspace{40mu} = {{{{\pi\eta}\underset{\underset{\phi_{k}}{︸}}{\sum\limits_{1 = {- \infty}}^{k - L - 1}{d_{1}{q\left( {t - {1T_{b}}} \right)}}}} + {{\pi\eta}{\sum\limits_{1 = {k - L}}^{k}{d_{1}{q\left( {t - {1T_{b}}} \right)}}}}}\mspace{40mu} = {\phi_{k} + {{\pi\eta}{\sum\limits_{1 = {k - L}}^{k}{d_{1}{{q\left( {t - {1T_{b}}} \right)}.}}}}}}}} & (10)\end{matrix}$

Accordingly, the phase variation in the interval [kT_(b), (k+1)T_(b)]depends on the phase angle φ_(k) at time t=(k−L−1)T_(b) and the datad_(k-L), d_(k-L+1), . . . , d_(k).

The condition for the zero crossings {t_(i)} is y(t_(i))=0. For a zerocrossing at t_(i) in the interval [kT_(b), (k+1)T_(b)], the followingholds true, therefore:

$\begin{matrix}{{{m\;\pi} = {{{\omega_{IF}t_{i}} + {\phi\left( t_{i} \right)}}\mspace{31mu} = {{\omega_{IF}t_{i}} + \phi_{k} + {{\pi\eta}{\sum\limits_{1 = {k - L}}^{k}{d_{1}{q\left( {t_{i} - {1T_{b}}} \right)}}}}}}}\mspace{14mu}{{{{where}\mspace{14mu} m} = 1},\ldots\mspace{14mu},M}} & (11)\end{matrix}$m must be incremented from 1 to M for as long as the corresponding zerocrossings t_(i) are still within the interval [kT_(b), (k+1)T_(b)].

Equation (11) defines the zero crossings t_(i) for GFSK-modulatedsignals via a non-linear relation. This leads to equation (11) being atranscendent equation which generally can be solved only withdifficulty—for example by iterative methods. Calculating thezero-crossing reference sequences on the basis of this equation isvirtually impossible in a receiver which can be used commercially.

According to the invention, the phase function q(t) is approximated by apiecewise linear function.

$\begin{matrix}{{q_{approx}(t)} = \left\{ \begin{matrix}{0,} & {x \leq 1} \\{{{\frac{1}{3}x} - \frac{1}{3}},} & {1 < x \leq 4} \\{1,} & {x > 4}\end{matrix} \right.} & (12)\end{matrix}$

The function q_(approx)(t) is shown by the curve 22 in FIG. 4.

If the piecewise linear function q_(approx)(t) according to equation(12), which applies to GFSK-modulated signals, is inserted in equation(11) for q(t), the following is obtained:

$\begin{matrix}\begin{matrix}{{m\;\pi} = {{\omega_{IF}t_{i}} + {\phi\left( t_{i} \right)}}} \\{= {{\omega_{IF}t_{i}} + \phi_{k} + {{\pi\eta}{\sum\limits_{1 = {k - L}}^{k}{d_{l}{q\left( {t_{i} - {l\; T_{b}}} \right)}}}}}} \\{= {{\omega_{IF}t_{i}} + \phi_{k} + {\frac{1}{3}{{\pi\eta}\begin{pmatrix}\begin{matrix}{{d_{k - 1}\left( {t_{i} - {\left( {k - 1} \right)T_{b}}} \right)} +} \\{{d_{k - 2}\left( {t_{i} - {\left( {k - 2} \right)T_{b}}} \right)} +}\end{matrix} \\{{d_{k - 3}\left( {t_{i} - {\left( {k - 3} \right)T_{b}}} \right)} - 1}\end{pmatrix}}}}}\end{matrix} & (13)\end{matrix}$

Transforming this relation, then

$\begin{matrix}{t_{i} = \frac{{\frac{1}{3}{{\pi\eta}\begin{pmatrix}{1 + {T_{b}\left( {{d_{k - 1}\left( {k - 1} \right)} +} \right.}} \\\left. {{d_{k - 2}\left( {k - 2} \right)} + {d_{k - 3}\left( {k - 3} \right)}} \right)\end{pmatrix}}} + {m\;\pi} - \phi_{k}}{\omega_{IF} + {\frac{1}{3}\pi\;{\eta\left( {d_{k - 1} + d_{k - 2} + d_{k - 3}} \right)}}}} & (14)\end{matrix}$is the solution for equation (11) using q_(approx)(t). Thus, the zeropoints t_(i) can be approximately calculated and the zero-crossingreference sequences {t_(i)} can be specified via a simple calculation(see equation (14)) which can be performed on-line.

It is pointed out that the demodulator 11 can be implemented indifferent ways and all such variations are contemplated as fallingwithin the scope of the present invention. A simple implementation isspecified in the document DE 102 14 581.4 and shown in FIG. 5. Thedetector 1 for zero crossings is followed by a counter 10′ which outputsa sequence of time intervals between successive zero crossing timest_delta_(i). The counter 10′ counts clock pulses that are suppliedthereto at a constant frequency f₀, and is reset with each zerocrossing. Before the counter 10′ is reset, the count t_delta_(i) reachedis output and stored in a shift register chain 13 following the counter10′.

Since the influence of a bit (symbol) is distributed over a number ofbit intervals (symbol intervals) when band-limited frequency modulationsuch as GMSK is used, it is appropriate to use all zero crossings inthis greater time interval, for detecting the associated bit. In GMSK,one bit influences the transmitting frequency over a time interval of 5bit periods. At an intermediate frequency of 1 MHz, the number of zerocrossings in this time interval is approximately 16. It is, therefore,appropriate to use 16 values for detecting one bit as is shown in FIG.5. These 16 zero crossings are thus determined not only by the bit to bedetected but also by the two preceding and two subsequent bits. It is,therefore, appropriate to determine not only 1 bit but a bit sequencefrom the successive zero crossings. In this example, 5 successive bitscan be determined from the 16 zero crossings.

The detection is carried out with the aid of a classification device 14which determines the distance of the zero-crossing sequence determinedin each case and stored in the shift register chain 3 with thezero-crossing reference sequences calculated by the unit 12 forcalculating zero-crossing sequences. The zero-crossing referencesequences are obtained in the manner described from the zero crossingsfor all possible bit sequences. If 5 successive bits are considered,2⁵=32 possible bit combinations are obtained as state variables for theFSM and thus corresponding zero-crossing reference sequences which mustbe compared with the zero-crossing sequence stored in the shift registerchain 13. The sequence of state variables which is correlated with thezero-crossing reference sequences having the shortest distance from thedetected zero-crossing sequence t_delta_(i) is detected as thetransmitted signal sequence d_(k). If this comparison is in each caseperformed in the space of one bit period, a total of 5 results areavailable for each bit. The classification device 14 can then determinethe detected bit in the time increment k, e.g. on the basis of amajority decision.

A method used in one embodiment of the invention for calculating thedistance between the zero-crossing distances t_delta_(i), stored in theshift register chain 13, and the zero-crossing distances {circumflexover (t)}_delta_(i) of the reference sequences consists in calculatingthe Euclidian distance norm according to the following relation

$\begin{matrix}{{d\left( {\left\{ {{t\_}{delta}}_{i} \right\},\left\{ {\hat{t}{\_{delta}}_{i}} \right\}} \right)} = \sqrt[g]{\sum\limits_{i = 1}^{M}{{{{t\_}{delta}}_{i} - {\hat{t}{\_{delta}}_{i}}}}^{g}}} & (15)\end{matrix}$where g=2 and M=16. A simplification of the calculation of the distancebetween the zero-crossing sequence measured and the zero-crossingreference sequences is obtained from the above relation for g=1 and iscalled “city block metric”.

Furthermore, in another embodiment, the demodulator 11 of FIG. 1 andFIG. 5 can perform a demodulation according to the Viterbi algorithm.The state variables of the FSM in this case define the states of atrellis diagram. As is known in the technology, e.g. in the field ofchannel decoding or channel equalization, Viterbi processing determinesthe shortest path through the trellis diagram. For this purpose, atransition metric (also called branch metric) is calculated for everypossible transition from a precursor state (time increment k) into atarget state (time increment k+1) of the trellis diagram. The transitionmetric is added to the state metric of the associated precursor state(ADD). Thus, state metrics are accumulated transition metric values. Thepossible state metric values of a target state, obtained at the varioustransitions into this particular target state, are compared (COMPAREoperation), and the path having the smallest state metric value for thetarget state considered is selected (SELECT operation). The remainingpaths are discarded. As is generally known, the ADD-COMPARE-SELECT (ACS)operations provide for an efficient and inexpensive determination of thetransmitted symbol sequence. To calculate the transition metric values,the Euclidian metric is normally used in the Viterbi algorithm.

While the invention has been illustrated and described with respect toone or more implementations, alterations and/or modifications may bemade to the illustrated examples without departing from the spirit andscope of the appended claims. In particular regard to the variousfunctions performed by the above described components or structures(assemblies, devices, circuits, systems, etc.), the terms (including areference to a “means”) used to describe such components are intended tocorrespond, unless otherwise indicated, to any component or structurewhich performs the specified function of the described component (e.g.,that is functionally equivalent), even though not structurallyequivalent to the disclosed structure which performs the function in theherein illustrated exemplary implementations of the invention. Inaddition, while a particular feature of the invention may have beendisclosed with respect to only one of several implementations, suchfeature may be combined with one or more other features of the otherimplementations as may be desired and advantageous for any given orparticular application. Furthermore, to the extent that the terms“including”, “includes”, “having”, “has”, “with”, or variants thereofare used in either the detailed description and the claims, such termsare intended to be inclusive in a manner similar to the term“comprising”.

1. A method for calculating zero-crossing reference sequences for thedata detection of a sequence of zero crossings of a received signal thatis based on a data symbol sequence angle-modulated signal, comprisingcalculating the zero-crossing reference sequences according to anequation specifying an output of a finite state machine that describessignal generation in a device, performing a demodulation by determininga transmitted data sequence by comparing the calculated zero-crossingreference sequences with a detected sequence of zero crossings, whereinthe comparing comprises comparing a part-sequence of finite length ofthe detected sequence of zero crossings with the zero-crossing referencesequences for each time increment, wherein a data symbol transmitted inthe time increment considered is determined by way of the comparison,and wherein determining the data symbol sequence is performed inaccordance with the Viterbi algorithm by processing a trellis diagramthat describes a state diagram of the finite state machine, for eachtime increment, wherein transition metric values between a precursorstate and a target state in the trellis diagram are calculated bycomparing the state-dependent zero-crossing reference sequences with thesequence of zero crossings detected for the time increment considered.2. The method of claim 1, further comprising using a modulation memoryof length L, with L≧2, to perform the angle-modulation at thetransmitter.
 3. The method of claim 1, wherein the angle-modulatedsignal is generated in accordance with a GFSK modulation method.
 4. Themethod of claim 1, wherein the angle-modulated signal is generated inaccordance with a binary FSK or MSK modulation method.
 5. The method ofclaim 1, wherein the finite state machine describes the signalgeneration in an approximate fashion.
 6. A method of demodulating areceived angle-modulated signal, comprising: detecting a sequence ofzero-crossings based on the received angle-modulated signal; generatinga plurality of zero-crossing reference sequences in accordance with apredetermined algorithm that is a function of a device performing theangle-modulation of the received signal; determining one or more datasymbols associated with the received signal by comparing the detectedsequence of zero-crossings with the plurality of zero-crossing referencesequences; and determining the one or more data symbols comprises:correlating the detected sequence of zero-crossings with the pluralityof zero-crossing reference sequences; selecting one of the zero-crossingreference sequences having a correlation associated with a predeterminedcriteria; and determining the one or more data symbols based on theselected zero-crossing reference sequence.
 7. The method of claim 6,wherein detecting the sequence of zero-crossings comprises: counting anumber of periodic pulses between successive zero-crossings for aplurality of zero-crossings; and generating a sequence of time intervalsassociated with the plurality of zero-crossings.
 8. The method of claim6, wherein generating the plurality of zero-crossing reference sequencescomprises: ascertaining a spectral impulse function associated with thedevice; ascertaining a phase function associated with the device; andcalculating the zero-crossing reference sequences using the spectralimpulse function and the phase function associated with the device. 9.The method of claim 8, further comprising ascertaining the phasefunction by approximating the phase function by a piecewise linearfunction.
 10. The method of claim 6, wherein correlating comprisescalculating a Euclidean distance between the detected sequence ofzero-crossings and each of the zero-crossing reference sequences. 11.The method of claim 10, wherein selecting one of the zero-crossingreference sequences comprises selecting the reference sequence havingthe smallest Euclidean distance from the detected sequence ofzero-crossings.